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Know Howe - Maximizing EV on MTGO


Josh Howe

About Josh Howe

I’m currently a graduate student working in the San Francisco Bay Area, and I play as much Magic: the Gathering as I can in my spare time.  I started playing around the release of Mirage, but played only sporadically until the release of Time Spiral.  At the time, I was doing my undergraduate work at Penn State and stumbled across a group of people drafting.  I was immediately hooked again, and in the years since, I’ve made it my goal to improve as much as a player as I reasonably am able to.  I’ve spent the past couple of years trying to grind my way onto the Pro Tour through PTQs, GPs, rating, or whatever other means might be available to me, and have had a handful of PTQ top 8s among other near misses along the way.

Know Howe – Maximizing EV on MTGO

Initially, I wanted to write about Scars of Mirrodin sealed deck, given that it’s the PTQ format for the next few months.  Unfortunately, my results thus far at Scars of Mirrodin sealed (though a very small sample space) have been almost entirely lackluster.  I’ve not had access to enough sealed deck events to really feel like I have been able to fix my weaknesses, and so I don’t find myself in a position to advise others on the new sealed deck format just yet.  That is about to change, though, as Scars of Mirrodin has become available on Magic: the Gathering Online (MTGO), and as a result the amount of sealed deck to which I’ll have access will increase enormously.

This increased access should mean I can play as many sealed deck events as I can reasonably find time for, but there’s one caveat, and it’s the reason most commonly cited when I ask others why they don’t play MTGO – cost.  As a graduate student, I have a fairly limited discretionary budget, which means I can’t actually guarantee that I may play MTGO as much as I am able to, especially if I also want to be able to play in local tournaments (which are basically a money sink and don’t have reasonable “freeroll” possibility) and PTQs (let alone budgeting for GP flights).  So when I play MTGO, I try to maximize the expected value (EV) of my choice in games as I imagine many players on a budget would like to.

In trying to maximize EV to “break into” MTGO so that I have an established account there that is profitable enough that playing requires minimal financial input, I have tried multiple approaches on multiple occasions, and I’m going to use that experience (along with some data provided by other friends who have tried similar things) to give some advice to those looking to get into MTGO, but unsure of how to do it without prohibitive financial commitment to virtual cards.  When I first started playing MTGO, it was rather daunting, but the environment quickly became something with which I was much more comfortable.  While this article is more about how to make choices maximizing EV on MTGO than it is about how to use MTGO, I’ll first discuss a little bit about the environment and getting started for those who are not familiar with it.

Learning MTGO

Setting up:  The first step is to download the necessary software and install it.  Once the software is installed and updated, you will have to create an account.  Unfortunately, there’s a cost associated with creating an account ($9.95), but the good news is that they give you a Magic 2010 booster (this seems like a strange choice, so I’d hope they’d update this to Magic 2011 at some point) and 2 Magic online Event Tickets (tix) among an assortment of other items (Planeswalker deck pack, avatars, et cetera).  The booster should be able to resell to dealer bots (more on this later) for ~3 tix (a pessimistic estimate, as at the time of writing Magic 2011 boosters are selling to bots for 3.36, although I can’t speak for Magic 2010), so the nominal cost seems to be about $5.

Learning the interface:  This is actually free, and it’s something that is quite worth doing.  With your starter product, you should be able to venture over to the new players area and get comfortable with the interface.  Go to Menu/Play/Casual Play/New Players.  Here you can join existing games waiting for players or create your own game, which another player will join.  I strongly suggest putting a few hours into this and learning how the MTGO interface works; it’s always frustrating to lose to clicking through combat, but it’s even more frustrating when it happens in a draft you paid to enter.  Other features worth investigating are the Collection tab (where you can see everything you own) and the Menu/Community/Marketplace/Classifieds tab (where trading happens).  One final thing to check out is the Menu/Settings tab, where you can (under Game Play) change where in the turn it will ask for priority passes.  As a note, these can also be changed by clicking on the appropriate part of the turn mid-game, but it’s good to establish a good base set of stops that suits your play needs (and so you’re not surprised when your opponent moves to combat and you don’t have a chance to use Blinding Mage to keep you from dying… which may have happened to me in one of my earlier drafts before I learned the interface).

The competitive offerings:  MTGO has a variety of competitive offerings, some of which are “standard fare” and offered all the time (or on a schedule) and others that are limited-time offerings for prerelease or release of new product.  There are various types of draft, sealed deck, and constructed events from which a player may choose.  Many of these I consider in the next section in the context of choosing events that maximize your EV as a player.

Maximizing EV

In order to evaluate EV, we need to consider the probability of winning a match so that we can project likely performance in a tournament.  In the subsequent analyses, I will use as an example a match win probability calculated from my performance in sanctioned events in the past year.  In order to calculate this match win probability, I’m counting only matches I’ve won or lost in the past year that are reported under the “Personal Information Center” portion of the DCI’s website by looking at the “Ratings History” tab under “Total Rating.”

As it turns out, in the past year, I’ve had 298 matches that have been sanctioned and have had either a win or loss result.  I’ve posted 200 wins, 98 losses, so my match win probability is just over 0.67; I’ll use 200/298 for my EV calculations.  There are a number of problems with this method:  the pool of people I’ve played is different from the pool of players on MTGO, this data considers also (dis)advantages from the human side of gaming that are not so relevant on MTGO, this assumes I’m as familiar with MTGO as I am with paper Magic and thus won’t make errors, and only 300 data points may not be enough for a great estimate of probability.  That said, I think this is the best means I have of calculating my win probability.  The opponents considered are those who choose to participate in sanctioned events and they come from a range of events from FNMs and prereleases up to Grand Prix.  I could add more data points, but I think 0.67 is probably a pretty fair estimate of a match win probability.  If you have another way you’d calculate your match win probability without a huge MTGO sample space (which would probably be a better way to do this exercise), please share it in the comments section.

In order to do the calculations, I’m going to use an Excel spreadsheet to calculate numbers, which I’ll report.  I’ll briefly outline the math used in each case (or reference how to do the calculation) so that if you’re not familiar with these sorts or probability calculations already, it shouldn’t be too difficult to reproduce these value or (more relevantly) calculate values to guide your own choices.

Since the events being considered have different costs, considering the likely nominal gain or loss (expected outcome minus entry fee) is less useful than considering the gain or loss scaled by the entry fee (expected value).

As a note, all analyses neglect the likely value of any cards received.  It is likely that you can resell some of the cards (or all of them) to bots or other players for some gain.  This is something to be considered as a small factor in the EV of an event, but it is neglected here.  Additionally, I’m neglecting any bonus swag (such as prerelease cards) and MOCS qualifier points that can be awarded.


There are three primary sorts of 8-man draft offerings on MTGO:  8-4s, 4-3-2-2s, and swiss.  The first two are single elimination, with the 8-4s giving 8 packs for 1st and 4 packs for 2nd place and the 4-3-2-2s comparably giving 4, 3, 2, and 2 packs for 1st through 4th place respectively.  Swiss drafts award one pack per match win, and each player has the option to play in up to 3 matches.

To calculate the expected outcome, find the probability of each outcome.  In the case of single elimination events, we need only consider the probability of winning some number of rounds (and no more) up to the maximum number of rounds.  The total probability must sum to 1, so using “P” to be the probability of winning, the probability of each outcome is:

0-1:  1-P (0.329)

1-1:  P-P2 (0.221)

2-1:  P2-P3 (0.148)

3-0:  P3 (0.302)

Multiply each outcome by the prize awarded for that outcome to find the probable outcome of an event.  In the case of an 8-4:

0.302*8+0.148*4 = 3.01 packs expected outcome

For a 4-3-2-2: 

0.302*4+0.148*3+0.221*2 = 2.10 packs expected outcome

To consider a swiss draft, a slightly different approach is needed, since losing a match does not end the event for you.  Thus, all matches end in either a win (with probability P) or a loss (with probability 1-P).  While there is only one way to go 3-0 or 0-3 (win or lose all matches), there are three ways each to go 2-1 or 1-2 (for 2-1 you can lose the first, second, or third match, and all return the same prize).  A general formula for the multiplicity factor by which we must weigh each outcome is: 

Multiplicity = Rounds!/(Wins!*Losses!), where “!” denotes a factorial.  4 factorial, for example, = 4*3*2*1 = 24, and 3 factorial = 3*2*1 = 6.  As a note, 0! = 1.

This gives the probability of each outcome as: 

0-3:  (1-P)3 (0.036)

1-2:  P*(1-P)2 (0.218)

2-1:  P2*(1-P) (0.444)

3-0:  P3 (0.302)

So the expected outcome is:

0.218*1+0.444*2+0.302*3 = 2.01 packs.

Since all drafts have the same entry fee, we can directly compare the outcomes and see that the 8-4 gives us the best value.  As a note, when P = 0.5, the outcome of both swiss and 8-4 is 1.5 packs, while 4-3-2-2 is 1.375.  For P < 0.5 swiss gives us the best expected outcome.  For P > 0.5 the 8-4 gives the best expected outcome.  For no value of P does the 4-3-2-2 return the best expected outcome.  To compare events with variable entry fee, we need a normalized way of looking at the returns we are likely to win.  So we define an expected value as the difference between event cost and expected outcome divided by the event cost.

In the case of drafts, the cost is generally 3 packs + 2 tix (although sometimes drafts are run on a “nix tix” or “tix only” basis and this will change the cost index… adjust calculations accordingly.  Because we rely on a dealer economy where packs we have or are selling are worth less than packs we want to acquire, I value prize packs at 3.5 tix  and packs for entry at 3.8 tix across the board.  Therefore, the cost of a draft is 3.8*3+2 = 13.4 tix

This gives us as expected value for each of the above cases:

8-4:  -0.213

4-3-2-2:  -0.453

Swiss:  -0.474

This value represents the likely return (in fractional tix) per tix put in.  Thus, for all drafts, we’re likely to lose money over time, but if we keep drafting, we lose money most slowly to drafting 8-4s.


Sealed events on MTGO are a bit more scarce than drafts, and they come in 4-pack and 6-pack variety.  The entry fee for 4-pack sealed is 4 boosters of the appropriate type, while for 6-pack the entry (in the case of prerelease sealed events) is 30 tix.  For 6-pack release sealed, the entry fee is 24 tix.  These events are typically less populated than drafts, and the offerings seem to change on a semi (ir)regular basis, so it’s good to keep an eye on what’s going on in sealed.  For the above three sorts, the expected outcomes and values are provided below:

4-pack:  These are 3-round swiss events and provide 5 packs for 3-0, 3 for 2-1, and 1 for 1-2.  Calculations are done analogously to those for the swiss drafts.

  • Expected outcome:  3.06 packs
  • Cost:  3.8*4 = 15.2 tix
  • EV:  -0.295

6-pack prerelease:  These are 4-round swiss events that provide 10 packs for 4-0, 4 for 3-1, and 1 for 2-2.  Calculations are again analogous to swiss drafts excepting that the multiplicity for 4-0 is 1, 3-1 is 4, and 2-2 is 6.

  • Expected outcome:  3.91 packs
  • Cost:  30 tix
  • EV:  -0.544

6-pack release:  These are 4-round swiss events that provide 13 packs for 4-0, 8 for 3-1, and 3 for 2-2.

  • Expected outcome:  6.70 packs
  • Cost:  24 tix
  • EV:  -0.024


Constructed events are a bit tricky, as they require a constructed deck to be owned in order to participate.  You need to evaluate how long a deck will likely be “good” along with how frequently you can play it and weigh its cost against these factors to decide if it is a good purchase.  For these analyses, I’m going to assume that we have the deck we’d like to play and will post the same win probabilities for consistency.  I don’t have as much faith in my analyses here as in the limited events due to these extra factors.

Constructed events are offered in “heads up” style (1 v. 1) and 8-player single-elimination.

Heads-up:  These cost 2 tix to enter and award 1 pack to the winner.

  • Expected outcome:  0.671 packs
  • Cost:  2 tix
  • EV:  0.174

8-player:  These cost 6 tix and award 5 packs for 1st, 3 for 2nd, and 2 each for 3rd and 4th.

  • Expected outcome:  2.4 packs
  • Cost:  6 tix
  • EV:  0.398

Additional Events

Other events are offered on MTGO such as premier events that have variable entries but fixed payouts.  The expected values of these types of events are harder to calculate because they have non-fixed numbers of entrants and fixed payouts for top performers.  They tend to be more top-heavy (so they reward players who have higher win probabilities), but the EV is based on the number of entrants and how many of them drop before they are out of prize contention.  For these, my recommendation is that you try to participate in ones on off-peak hours, as the entry numbers in these tend to be lower so your EV is requisitely higher since fewer people are sharing more payout.

One final event type that is a fixed-entry event is a release event draft, the “64-player ‘Top 8’ Premier draft.”  These drafts have a fixed entry of 64 players and are played in eight 8-player pods that cut a winner from each pod to compete in a “Top 8” draft.  The events are single elimination with payouts of 20 packs for 1st, 15 for 2nd, 10 for 3rd-4th, 6 for 5th-8th, 4 for 9th-16th, and 2 for 17th-32nd.  Cost to enter is 4 tix + 3 packs.  Calculations are done as if for a 6-round single-elimination draft.

  • Expected outcome:  4.80 packs
  • Cost:  15.4 tix
  • EV:  0.090


Overall, the constructed events return the highest EV.  This is not unexpected, because the overhead cost of a deck is not factored into the event entry costs.  In fact, it makes sense that if you play with a constructed deck (that is viable) enough, you can make the money back that you spent on the deck.  The problem with constructed on MTGO as a source of maximizing EV is that it requires a lot of time and play to make back the cost of the deck.  If you’ve got a lot of time to play and the equity to put into a deck up front, then this is likely the best way to go about it.  You can buy cards from and resell cards to bots without major losses, so you can have a fairly dynamic deck without too much expectation of financial loss, and a lot of play in 8-man queues should be a good way to profit from your investment.

In limited events, two events stand out from the rest:  release event 64-player drafts and release event 16-player sealeds.  Both of these events happen only for a two-week window around the launch of a set.  Scars of Mirrodin release events run October 20th through November 3rd, so now is a particularly convenient time to be doing limited online.  While the EV on the sealed event with highest EV is still negative by about 2 cents per dollar (in the case of the winning probability used here), the value of cards opened should more than compensate for that minor loss of value.

In the case of M11, I played the release event sealed deck tournaments almost exclusively during the lead-up to Grand Prix:  Portland for practice.  I put about $40 into MTGO and used it to fund my play and have yet to redeposit.  I am left with a nearly complete M11 set (which I can easily complete to “cash out” as a physical set if I’d like in order to recoup the financial investment), which I can also use as a reasonable basis for starting a constructed deck.  I plan to use the same approach to practice for PTQs with Scars of Mirrodin release events.

If I had to prescribe a “maximum EV” approach to MTGO, it would be the following:

During set release event windows, “grind” 64-player drafts and 16-player sealed queues.  Use these to build sets to either build constructed decks or cash out, depending on needs.  Early on in the set, resell cards to bots frequently (as values tend to start inflated due to need for players looking to play constructed immediately), but curtail this once prices begin to relax to complete sets if that’s something of interest to you.  Generally, completing sets and cashing them out and reselling the paper copies is more lucrative than selling the singles off to bots, so if you can make this work, it’s your best option.

After release events, use the equity gained in your collection through grinding to put together a constructed deck, and use this to grind the 8-player constructed queues.

While these numbers are not valid for everyone, I encourage you to do these calculations with your results if you want “more accurate” numbers.  In general, the results I found for myself should not be atypical.  In fact, most of you will likely find the same outcomes – the limited events that I prescribe as “highest EV” are so much more lucrative in prize structure that the dependence of relative EV between these and other events on win probability actually weakens.  That said, one case where knowing your win probability can really help is if you want to practice drafting.  All else aside, there can be a case for doing swiss (or 4-3-2-2) drafts rather than 8-4s if you just need bulk practice for minimal costs.  Granted, the mean player skill level changes between these drafts and it may change both your win percentages and the relevance of your practice, so bear this in mind.

Hopefully you have found this to be insightful and have found that it has provided a reasonable case for these sorts of analyses in terms of the value of various tournament offerings.  I personally find these analyses to be useful when determining whether or not to participate in events.  Granted, there are always intangibles for events in person (and even online) such as gain to play skill through practice.  These things have value.  A Grand Prix tournament will seldom have a positive EV unless you happen to live in an area of the world with small GPs and one shows up in your back yard – I still advocate traveling to and attending these because they are just that much fun.  But for online events, where the enjoyment is more marginal and the practice value is comparable between variable offerings, the financial EV is a good test for how worthwhile an event likely is.  While my time to play MTGO is quite limited right now due to academic commitments, I will be grinding Scars sealed deck as much as possible during the two weeks of high EV release events.  I hope to see some of you in the queues!  As always, please feel free to leave comments, in this case especially if you think I have made an error or overlooked something major.

Josh Howe

Maniacal42 on MTGO

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